Finite Group Databasebeta

← #30595519

Subgroups — #30595519

Order 15616.

516 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461675C211yesmaximal, characteristic
2#21461545C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21448301C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×#14519832—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519736C411yescharacteristic
13C22×C4×Dic61C2211yescharacteristic
14#16839658C411yescharacteristic
15#16839658C411yescharacteristic
16#16839658C2211yescharacteristic
17#16839658C2211yescharacteristic
18#16839634—21no—
19#16839634—21no—
20C4×#11758196—21no—
21C4×#11758196—21no—
22C2×#117×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C22⋊#92420—24no—
27C22⋊#92420—42no—
28#14519832—42no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519736—22no—
32#14519736—22no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51#117×C61—42no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C42×C61—21no—
56C24×C61C22⋊C411yescharacteristic
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×#92420—24no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—42no—
87C42×C61—42no—
88C22⋊Dic61—24no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61M1612yes—
92C4⋊Dic61M1612yes—
93#11758196—42no—
94#11758196—42no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—24no—
99C4×Dic61—22no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61#10112yes—
110C23×C61C2×C22⋊C411yescharacteristic
111C2×C4×C61—24no—
112C2×C4×C61—24no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#9912yes—
124C2×C4×C61C2×M1611yescharacteristic
125C2×C4×C61C2×M1611yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—44no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#10412yes—
145C2×Dic61#13512yes—
146C2×Dic61AGL(1,ℤ/8)11yescharacteristic
147C2×Dic61#13711yescharacteristic
148#92420—44no—
149#92420—82no—
150#7613—611nomaximal, Sylow
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61#40711yescharacteristic
159C22×C61C2×#9911yescharacteristic
160C22×C61C2×#10111yescharacteristic
161C22×C61#41611yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61#42111yescharacteristic
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—81no—
169C4×C61—81no—
170Dic61—22no—
171Dic61—22no—
172Dic61—21no—
173Dic61—21no—
174Dic61—42no—
175Dic61—42no—
176Dic61—41no—
177#2296—611no—
178#1797—611no—
179#1749—611no—
180#1271—612no—
181#1271—612no—
182C2×C61—42no—
183C2×C61#146311yescharacteristic
184C2×C61#148811yescharacteristic
185C2×C61#148911yescharacteristic
186C2×C61#150111yescharacteristic
187C2×C61#151311yescharacteristic
188C2×C61#153111yescharacteristic
189C2×C61#155211yescharacteristic
190C2×#117—611no—
191C2×#117#692311yescharacteristic
192C22×C42—611no—
193C2×C4⋊C8—1221no—
194C2×C22⋊C8—1221no—
195C2×C22⋊C8—1221no—
196C2×#97—1221no—
197#389—611no—
198#389—611no—
199#389—611no—
200#389—611no—
201#385—1221no—
202#385—1221no—
203C4×C4⋊C4—1221no—
204C4×C4⋊C4—1221no—
205#336—612no—
206#336—612no—
207C61#761311yescharacteristic, complemented, Sylow
208C23×C4—611no—
209C23×C4—611no—
210C23×C4C2×#692311yescharacteristic
211C22×C8—1222no—
212C22×C8—1222no—
213#117—42no—
214#117—1222no—
215#117—1222no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C4⋊C4C2×#692311yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—1221no—
226C2×C42—21no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—1221no—
232C2×C42—2442no—
233C4⋊C8—2442no—
234C22⋊C8—1224no—
235C22⋊C8—2442no—
236#97—2442no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24C22⋊#692311yescharacteristic
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1222no—
253C22×C4—1221no—
254C22×C4—1222no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—2441no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4C22⋊#692311yescharacteristic
262C22×C4C22×#692311yescharacteristic
263C2×C8—1224no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2442no—
267C2×C8—2442no—
268C2×C8—2442no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—612no—
272C4⋊C4—612no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—2442no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2442no—
279C4⋊C4—2442no—
280C22⋊C4—42no—
281C22⋊C4—1224no—
282C42—42no—
283C42—1224no—
284C42—1222no—
285C42—1222no—
286C42—2441no—
287C42—2441no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#1451983812yes—
295C23C2×C22⋊#692311yescharacteristic
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—612no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—612no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2444no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4#1451983512yes—
331C2×C4D61⋊M1611yescharacteristic
332C2×C4D61⋊M1611yescharacteristic
333C8—4882no—
334C8—2444no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22#1684073411yescharacteristic
343C22C2×#1451983511yescharacteristic
344C22C2×#1451983811yescharacteristic
345C22#1684075211yescharacteristic
346C22#1684075311yescharacteristic
347C22D61⋊#10411yescharacteristic
348C22#1684075911yescharacteristic
349C4—22no—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—81no—
354C4—1222no—
355C4—1222no—
356C4—1221no—
357C4—1221no—
358C4—2442no—
359C4—2442no—
360C4—2441no—
361C2—42no—
362C2#2146106911yescharacteristic
363C2#2146115211yescharacteristic
364C2#2146115611yescharacteristic
365C2#2146119411yescharacteristic
366C2#2146123411yescharacteristic
367C2#2146129111yescharacteristic
368C2#2146134011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#7613
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21460638C2semidirect
4. #21460638C2semidirect
207. C61#7613semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214616752
#214615452
#214606382
#214483012
#761361